1
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See Toh JH, Du M, Tang X, Su Y, Rojo T, Patterson CO, Williams NR, Zhang C, Gupta S. Interaction Effects on the Dynamical Anderson Metal-Insulator Transition Using Kicked Quantum Gases. PHYSICAL REVIEW LETTERS 2024; 133:076301. [PMID: 39213552 DOI: 10.1103/physrevlett.133.076301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Revised: 06/12/2024] [Accepted: 07/12/2024] [Indexed: 09/04/2024]
Abstract
Understanding the interplay of interaction and disorder in quantum transport poses long-standing scientific challenges for theory and experiment. While highly controlled ultracold atomic platforms combining atomic interactions with spatially disordered lattices have led to remarkable advances, the extension of such controlled studies to phenomena in high-dimensional disordered systems, such as the three-dimensional Anderson metal-insulator transition has been limited. Kicked quantum gases provide an alternate experimental platform that captures the Anderson model in momentum space and features dynamical localization as the analog of Anderson localization. Here, we utilize a momentum space lattice platform using quasiperiodically kicked ultracold atomic gases to experimentally investigate interaction effects on the three-dimensional dynamical Anderson metal-insulator transition. We observe interaction-driven subdiffusion and a divergence of delocalization onset time on approaching the phase boundary. Mean-field numerical simulations show qualitative agreement with experimental observations, but with significant quantitative deviations.
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2
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Hopjan M, Vidmar L. Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models. ENTROPY (BASEL, SWITZERLAND) 2024; 26:656. [PMID: 39202126 PMCID: PMC11354069 DOI: 10.3390/e26080656] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/03/2024] [Revised: 07/28/2024] [Accepted: 07/29/2024] [Indexed: 09/03/2024]
Abstract
We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in the site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of single-particle states. We then generalize our statement to a similar relationship between the non-equal time and space density correlation functions in many-body states, and the transition probabilities of single-particle states at nonzero distances. Finally, we study the equal-time connected density-density correlation functions in many-body states, which exhibit certain qualitative analogies with the survival and transition probabilities of single-particle states. Our results are numerically tested for two paradigmatic models of single-particle localization: the 3D Anderson model and the 1D Aubry-André model. This work gives an affirmative answer to the question of whether it is possible to measure features of single-particle survival and transition probabilities by the dynamics of observables in many-body states.
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Affiliation(s)
- Miroslav Hopjan
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia;
| | - Lev Vidmar
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia;
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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3
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Yao Y, Xiang L. Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium. ENTROPY (BASEL, SWITZERLAND) 2024; 26:592. [PMID: 39056954 PMCID: PMC11275873 DOI: 10.3390/e26070592] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2024] [Revised: 07/07/2024] [Accepted: 07/09/2024] [Indexed: 07/28/2024]
Abstract
Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the most promising physical realizations to achieve the long-term goal of building fault-tolerant quantum computers. The past decade has witnessed the rapid development of this field, where many intermediate-scale multi-qubit experiments emerged to simulate nonequilibrium quantum many-body dynamics that are challenging for classical computers. Here, we review the basic concepts of superconducting quantum simulation and their recent experimental progress in exploring exotic nonequilibrium quantum phenomena emerging in strongly interacting many-body systems, e.g., many-body localization, quantum many-body scars, and discrete time crystals. We further discuss the prospects of quantum simulation experiments to truly solve open problems in nonequilibrium many-body systems.
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Affiliation(s)
- Yunyan Yao
- ZJU-Hangzhou Global Scientific and Technological Innovation Center, Department of Physics, Zhejiang University, Hangzhou 311200, China
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4
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Zhou XC, Wang Y, Poon TFJ, Zhou Q, Liu XJ. Exact New Mobility Edges between Critical and Localized States. PHYSICAL REVIEW LETTERS 2023; 131:176401. [PMID: 37955469 DOI: 10.1103/physrevlett.131.176401] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Revised: 08/25/2023] [Accepted: 09/29/2023] [Indexed: 11/14/2023]
Abstract
The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization. Here the robustness refers to the stability against both single-particle perturbation and interactions in the few-body regime. The exactly solvable one-dimensional models are featured by a quasiperiodic mosaic type of both hopping terms and on-site potentials. The analytic results enable us to unambiguously obtain the critical states which otherwise require arduous numerical verification including the careful finite size scalings. The critical states and new MEs are shown to be robust, illustrating a generic mechanism unveiled here that the critical states are protected by zeros of quasiperiodic hopping terms in the thermodynamic limit. Further, we propose a novel experimental scheme to realize the exactly solvable model and the new MEs in an incommensurate Rydberg Raman superarray. This Letter may pave a way to precisely explore the critical states and new ME physics with experimental feasibility.
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Affiliation(s)
- Xin-Chi Zhou
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
| | - Yongjian Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
- School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China
| | - Ting-Fung Jeffrey Poon
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
| | - Qi Zhou
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
- International Quantum Academy, Shenzhen 518048, China
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5
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Vallejo-Fabila I, Torres-Herrera EJ. Late-time universal distribution functions of observables in one-dimensional many-body quantum systems. Phys Rev E 2023; 108:044102. [PMID: 37978615 DOI: 10.1103/physreve.108.044102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 09/12/2023] [Indexed: 11/19/2023]
Abstract
We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return probability and its version for a completely extended initial state, the so-called spectral form factor. We complement our analysis with the spin autocorrelation and connected spin-spin correlation functions, both of interest in experiments with quantum simulators. We show that the distribution function has a universal shape provided the central limit theorem holds. Explicitly, the shape is exponential for the return probability and spectral form factor, meanwhile it is Gaussian for the few-body observables. We also discuss implications over the so-called many-body localization. Remarkably, our approach requires only a single sample of the dynamics and small system sizes, which could be quite advantageous when dealing specially with disordered systems.
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Affiliation(s)
- I Vallejo-Fabila
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla, 72570, México
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6
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Kudo K. Localization Detection Based on Quantum Dynamics. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1085. [PMID: 36010749 PMCID: PMC9407476 DOI: 10.3390/e24081085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Revised: 08/04/2022] [Accepted: 08/04/2022] [Indexed: 06/15/2023]
Abstract
Detecting many-body localization (MBL) typically requires the calculation of high-energy eigenstates using numerical approaches. This study investigates methods that assume the use of a quantum device to detect disorder-induced localization. Numerical simulations for small systems demonstrate how the magnetization and twist overlap, which can be easily obtained from the measurement of qubits in a quantum device, changing from the thermal phase to the localized phase. The twist overlap evaluated using the wave function at the end of the time evolution behaves similarly to the one evaluated with eigenstates in the middle of the energy spectrum under a specific condition. The twist overlap evaluated using the wave function after time evolution for many disorder realizations is a promising probe for detecting MBL in quantum computing approaches.
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Affiliation(s)
- Kazue Kudo
- Department of Computer Science, Ochanomizu University, Tokyo 112-8610, Japan;
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
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7
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Vu D, Huang K, Li X, Das Sarma S. Fermionic Many-Body Localization for Random and Quasiperiodic Systems in the Presence of Short- and Long-Range Interactions. PHYSICAL REVIEW LETTERS 2022; 128:146601. [PMID: 35476495 DOI: 10.1103/physrevlett.128.146601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Revised: 12/06/2021] [Accepted: 03/20/2022] [Indexed: 06/14/2023]
Abstract
We study many-body localization (MBL) for interacting one-dimensional lattice fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing on the role of interaction range. We obtain the MBL quantum phase diagrams by calculating the experimentally relevant inverse participation ratio (IPR) at half-filling using exact diagonalization methods and extrapolating to the infinite system size. For short-range interactions, our results produce in the phase diagram a qualitative symmetry between weak and strong interaction limits. For long-range interactions, no such symmetry exists as the strongly interacting system is always many-body localized, independent of the effective disorder strength, and the system is analogous to a pinned Wigner crystal. We obtain various scaling exponents for the IPR, suggesting conditions for different MBL regimes arising from interaction effects.
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Affiliation(s)
- DinhDuy Vu
- Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
| | - Ke Huang
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong SAR
| | - Xiao Li
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong SAR
- City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, Guangdong, China
| | - S Das Sarma
- Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
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8
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One-Dimensional Disordered Bosonic Systems. ATOMS 2021. [DOI: 10.3390/atoms9040112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.
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9
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Guo Q, Cheng C, Li H, Xu S, Zhang P, Wang Z, Song C, Liu W, Ren W, Dong H, Mondaini R, Wang H. Stark Many-Body Localization on a Superconducting Quantum Processor. PHYSICAL REVIEW LETTERS 2021; 127:240502. [PMID: 34951777 DOI: 10.1103/physrevlett.127.240502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
Quantum emulators, owing to their large degree of tunability and control, allow the observation of fine aspects of closed quantum many-body systems, as either the regime where thermalization takes place or when it is halted by the presence of disorder. The latter, dubbed many-body localization (MBL) phenomenon, describes the nonergodic behavior that is dynamically identified by the preservation of local information and slow entanglement growth. Here, we provide a precise observation of this same phenomenology in the case where the quenched on-site energy landscape is not disordered, but rather linearly varied, emulating the Stark MBL. To this end, we construct a quantum device composed of 29 functional superconducting qubits, faithfully reproducing the relaxation dynamics of a nonintegrable spin model. At large Stark potentials, local observables display periodic Bloch oscillations, a manifesting characteristic of the fragmentation of the Hilbert space in sectors that conserve dipole moments. The flexible programmability of our quantum emulator highlights its potential in helping the understanding of nontrivial quantum many-body problems, in direct complement to simulations in classical computers.
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Affiliation(s)
- Qiujiang Guo
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Chen Cheng
- School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
- Beijing Computational Science Research Center, Beijing 100094, China
| | - Hekang Li
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Shibo Xu
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Pengfei Zhang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhen Wang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Chao Song
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Wuxin Liu
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Wenhui Ren
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Hang Dong
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Rubem Mondaini
- Beijing Computational Science Research Center, Beijing 100094, China
| | - H Wang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
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10
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Sierant P, Lazo EG, Dalmonte M, Scardicchio A, Zakrzewski J. Constraint-Induced Delocalization. PHYSICAL REVIEW LETTERS 2021; 127:126603. [PMID: 34597060 DOI: 10.1103/physrevlett.127.126603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
We study the impact of quenched disorder on the dynamics of locally constrained quantum spin chains, that describe 1D arrays of Rydberg atoms in both the frozen (Ising-type) and dressed (XY-type) regime. Performing large-scale numerical experiments, we observe no trace of many-body localization even at large disorder. Analyzing the role of quenched disorder terms in constrained systems we show that they act in two, distinct and competing ways: as an on-site disorder term for the basic excitations of the system, and as an interaction between excitations. The two contributions are of the same order, and as they compete (one towards localization, the other against it), one does never enter a truly strong disorder, weak interaction limit, where many-body localization occurs. Such a mechanism is further clarified in the case of XY-type constrained models: there, a term which would represent a bona fide local quenched disorder term acting on the excitations of the clean model must be written as a series of nonlocal terms in the unconstrained variables. Our observations provide a simple picture to interpret the role of quenched disorder that could be immediately extended to other constrained models or quenched gauge theories.
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Affiliation(s)
- Piotr Sierant
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Eduardo Gonzalez Lazo
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea, 265, 34136 Trieste, Italy
| | - Marcello Dalmonte
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea, 265, 34136 Trieste, Italy
| | - Antonello Scardicchio
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- INFN Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
- Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
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11
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Wang Y, Cheng C, Liu XJ, Yu D. Many-Body Critical Phase: Extended and Nonthermal. PHYSICAL REVIEW LETTERS 2021; 126:080602. [PMID: 33709721 DOI: 10.1103/physrevlett.126.080602] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2019] [Revised: 08/10/2020] [Accepted: 02/02/2021] [Indexed: 06/12/2023]
Abstract
The transition between ergodic and many-body localization (MBL) phases lies at the heart of understanding quantum thermalization of many-body systems. Here, we predict a many-body critical (MBC) phase with finite-size scaling analysis in the one-dimensional extended Aubry-André-Harper-Hubbard model, which is different from both the ergodic phase and MBL phase, implying that the quantum system hosts three different fundamental phases in the thermodynamic limit. The level statistics in the MBC phase are well characterized by the so-called critical statistics, and the wave functions exhibit deep multifractal behavior only in the critical region. We further study the half-chain entanglement entropy and thermalization properties and show that the former, in the MBC phase, manifest a volume law scaling, while the many-body states violate the eigenstate thermalization hypothesis. The results are confirmed by the state-of-the-art numerical calculations with system size up to L=22. This work unveils a novel many-body phase which is extended but nonthermal.
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Affiliation(s)
- Yucheng Wang
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Chen Cheng
- School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
| | - Xiong-Jun Liu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Dapeng Yu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
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12
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Torres-Herrera EJ, Vallejo-Fabila I, Martínez-Mendoza AJ, Santos LF. Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions. Phys Rev E 2021; 102:062126. [PMID: 33465957 DOI: 10.1103/physreve.102.062126] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Accepted: 11/10/2020] [Indexed: 11/07/2022]
Abstract
In a disordered system, a quantity is self-averaging when the ratio between its variance for disorder realizations and the square of its mean decreases as the system size increases. Here, we consider a chaotic disordered many-body quantum system and search for a relationship between self-averaging behavior and the properties of the distributions over disorder realizations of various quantities and at different timescales. An exponential distribution, as found for the survival probability at long times, explains its lack of self-averaging, since the mean and the dispersion are equal. Gaussian distributions, however, are obtained for both self-averaging and non-self-averaging quantities. Our studies show also that one can make conclusions about the self-averaging behavior of one quantity based on the distribution of another related quantity. This strategy allows for semianalytical results, and thus circumvents the limitations of numerical scaling analysis, which are restricted to few system sizes.
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Affiliation(s)
- E Jonathan Torres-Herrera
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apt. Postal J-48, Puebla 72570, Mexico
| | - Isaías Vallejo-Fabila
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apt. Postal J-48, Puebla 72570, Mexico
| | - Andrei J Martínez-Mendoza
- División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/Instituto Tecnológico de Oaxaca, C.P. 68030, Oaxaca de Juárez, Mexico
| | - Lea F Santos
- Department of Physics, Yeshiva University, New York City, New York 10016, USA
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13
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Wang Y, Xia X, Zhang L, Yao H, Chen S, You J, Zhou Q, Liu XJ. One-Dimensional Quasiperiodic Mosaic Lattice with Exact Mobility Edges. PHYSICAL REVIEW LETTERS 2020; 125:196604. [PMID: 33216579 DOI: 10.1103/physrevlett.125.196604] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Revised: 08/30/2020] [Accepted: 10/15/2020] [Indexed: 06/11/2023]
Abstract
The mobility edges (MEs) in energy that separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results that allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of all states in the spectra, as derived through computing the Lyapunov exponents from Avila's global theory and also numerically verified by calculating the fractal dimension. We further propose a novel scheme with experimental feasibility to realize our model based on an optical Raman lattice, which paves the way for experimental exploration of the predicted exact ME physics.
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Affiliation(s)
- Yucheng Wang
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xu Xia
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Long Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Hepeng Yao
- CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay 91128 Palaiseau, France
| | - Shu Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Yangtze River Delta Physics Research Center, Liyang, Jiangsu 213300, China
| | - Jiangong You
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Qi Zhou
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Xiong-Jun Liu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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14
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Sinha S, Sinha S. Chaos and Quantum Scars in Bose-Josephson Junction Coupled to a Bosonic Mode. PHYSICAL REVIEW LETTERS 2020; 125:134101. [PMID: 33034498 DOI: 10.1103/physrevlett.125.134101] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Accepted: 08/31/2020] [Indexed: 06/11/2023]
Abstract
We consider a model describing Bose-Josephson junction (BJJ) coupled to a single bosonic mode exhibiting quantum phase transition (QPT). Onset of chaos above QPT is observed from semiclassical dynamics as well from spectral statistics. Based on entanglement entropy, we analyze the ergodic behavior of eigenstates with increasing energy density which also reveals the influence of dynamical steady state known as π-mode on it. We identify the imprint of unstable π-oscillation as many body quantum scar (MBQS), which leads to the deviation from ergodicity and quantify the degree of scarring. Persistence of phase coherence in nonequilibrium dynamics of such initial state corresponding to the π-mode is an observable signature of MBQS which has relevance in experiments on BJJ.
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Affiliation(s)
- Sudip Sinha
- Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia 741246, India
| | - S Sinha
- Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia 741246, India
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15
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Lenarčič Z, Alberton O, Rosch A, Altman E. Critical Behavior near the Many-Body Localization Transition in Driven Open Systems. PHYSICAL REVIEW LETTERS 2020; 125:116601. [PMID: 32976013 DOI: 10.1103/physrevlett.125.116601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Accepted: 08/12/2020] [Indexed: 06/11/2023]
Abstract
Coupling a many-body localized system to a thermal bath breaks local conservation laws and washes out signatures of localization. When the bath is nonthermal or when the system is also weakly driven, local conserved quantities acquire a highly nonthermal stationary value. We demonstrate how this property can be used to study the many-body localization phase transition in weakly open systems. Here, the strength of the coupling to the nonthermal baths plays a similar role as a finite temperature in a T=0 quantum phase transition. By tuning this parameter, we can detect key features of the many-body localization (MBL) transition: the divergence of the dynamical exponent due to Griffiths effects in one dimension and the critical disorder strength. We apply these ideas to study the MBL critical point numerically. The possibility to observe critical signatures of the MBL transition in an open system allows for new numerical approaches that overcome the limitations of exact diagonalization studies. Here, we propose a scalable numerical scheme to study the MBL critical point using matrix-product operator solution to the Lindblad equation.
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Affiliation(s)
- Zala Lenarčič
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Ori Alberton
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - Achim Rosch
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - Ehud Altman
- Department of Physics, University of California, Berkeley, California 94720, USA
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16
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Wang Y, Zhang L, Niu S, Yu D, Liu XJ. Realization and Detection of Nonergodic Critical Phases in an Optical Raman Lattice. PHYSICAL REVIEW LETTERS 2020; 125:073204. [PMID: 32857567 DOI: 10.1103/physrevlett.125.073204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 07/21/2020] [Indexed: 06/11/2023]
Abstract
The critical phases, being delocalized but nonergodic, are fundamental phases different from both the many-body localization and ergodic extended quantum phases, and have so far not been realized in experiment. Here we propose an incommensurate topological insulating model of AIII symmetry class to realize such critical phases through an optical Raman lattice scheme, which possesses a one-dimensional (1D) spin-orbit coupling and an incommensurate Zeeman potential. We show the existence of both noninteracting and many-body critical phases, which can coexist with the topological phase, and show that the critical-localization transition coincides with the topological phase boundary in noninteracting regime. The dynamical detection of the critical phases is proposed and studied in detail based on the available experimental techniques. Finally, we demonstrate how the proposed critical phases can be achieved within the current ultracold atom experiments. This work paves the way to observe the novel critical phases.
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Affiliation(s)
- Yucheng Wang
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Long Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Sen Niu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Dapeng Yu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiong-Jun Liu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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17
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Deng X, Masella G, Pupillo G, Santos L. Universal Algebraic Growth of Entanglement Entropy in Many-Body Localized Systems with Power-Law Interactions. PHYSICAL REVIEW LETTERS 2020; 125:010401. [PMID: 32678649 DOI: 10.1103/physrevlett.125.010401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Revised: 05/18/2020] [Accepted: 06/16/2020] [Indexed: 06/11/2023]
Abstract
Power-law interactions play a key role in a large variety of physical systems. In the presence of disorder, these systems may undergo many-body localization for a sufficiently large disorder. Within the many-body localized phase the system presents in time an algebraic growth of entanglement entropy, S_{vN}(t)∝t^{γ}. Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent γ acquires a universal value γ_{c}≃0.33 at the many-body localization transition, for different lattice models, decay powers, filling factors, or initial conditions. Moreover, our results suggest an intriguing relation between γ_{c} and the critical minimal decay power of interactions necessary for many-body localization.
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Affiliation(s)
- Xiaolong Deng
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
| | - Guido Masella
- ISIS (UMR 7006) and icFRC, University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - Guido Pupillo
- ISIS (UMR 7006) and icFRC, University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
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18
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Sahu S, Xu S, Swingle B. Scrambling Dynamics across a Thermalization-Localization Quantum Phase Transition. PHYSICAL REVIEW LETTERS 2019; 123:165902. [PMID: 31702346 DOI: 10.1103/physrevlett.123.165902] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Revised: 08/17/2019] [Indexed: 06/10/2023]
Abstract
We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with subballistic operator spreading. The critical disorder strength for the ballistic to subballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the transition from subballistic to logarithmic behavior at the actual eigenstate localization transition is not resolved in our finite numerics. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.
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Affiliation(s)
- Subhayan Sahu
- Condensed Matter Theory Center and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Shenglong Xu
- Condensed Matter Theory Center and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Brian Swingle
- Condensed Matter Theory Center, Maryland Center for Fundamental Physics, Joint Center for Quantum Information and Computer Science, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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19
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Rispoli M, Lukin A, Schittko R, Kim S, Tai ME, Léonard J, Greiner M. Quantum critical behaviour at the many-body localization transition. Nature 2019; 573:385-389. [DOI: 10.1038/s41586-019-1527-2] [Citation(s) in RCA: 81] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2018] [Accepted: 07/03/2019] [Indexed: 11/09/2022]
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20
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Deng X, Ray S, Sinha S, Shlyapnikov GV, Santos L. One-Dimensional Quasicrystals with Power-Law Hopping. PHYSICAL REVIEW LETTERS 2019; 123:025301. [PMID: 31386526 DOI: 10.1103/physrevlett.123.025301] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2018] [Revised: 01/04/2019] [Indexed: 06/10/2023]
Abstract
One-dimensional quasiperiodic systems with power-law hopping, 1/r^{a}, differ from both the standard Aubry-André (AA) model and from power-law systems with uncorrelated disorder. Whereas in the AA model all single-particle states undergo a transition from ergodic to localized at a critical quasidisorder strength, short-range power-law hops with a>1 can result in mobility edges. We find that there is no localization for long-range hops with a≤1, in contrast to the case of uncorrelated disorder. Systems with long-range hops rather present ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but nonergodic) states. Both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.
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Affiliation(s)
- X Deng
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover, Germany
| | - S Ray
- Indian Institute of Science Education and Research, Kolkata, Mohanpur, Nadia 741246, India
| | - S Sinha
- Indian Institute of Science Education and Research, Kolkata, Mohanpur, Nadia 741246, India
| | - G V Shlyapnikov
- LPTMS, CNRS, Universite Paris Sud, Universite Paris-Saclay, Orsay 91405, France
- SPEC, CEA, CNRS, Universite Paris-Saclay, CEA Saclay, Gif sur Yvette 91191, France
- Russian Quantum Center, Skolkovo, Moscow 143025, Russia
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
- Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 430071 Wuhan, China
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover, Germany
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21
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Mierzejewski M, Prelovšek P, Bonča J. Einstein Relation for a Driven Disordered Quantum Chain in the Subdiffusive Regime. PHYSICAL REVIEW LETTERS 2019; 122:206601. [PMID: 31172751 DOI: 10.1103/physrevlett.122.206601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2018] [Indexed: 06/09/2023]
Abstract
A quantum particle propagates subdiffusively on a strongly disordered chain when it is coupled to itinerant hard-core bosons. We establish a generalized Einstein relation (GER) that relates such subdiffusive spread to an unusual time-dependent drift velocity, which appears as a consequence of a constant electric field. We show that GER remains valid much beyond the regime of the linear response. Qualitatively, it holds true up to strongest drivings when the nonlinear field effects lead to the Stark-like localization. Numerical calculations based on full quantum evolution are substantiated by much simpler rate equations for the boson-assisted transitions between localized Anderson states.
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Affiliation(s)
- M Mierzejewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - P Prelovšek
- J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - J Bonča
- J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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22
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van Nieuwenburg E, Baum Y, Refael G. From Bloch oscillations to many-body localization in clean interacting systems. Proc Natl Acad Sci U S A 2019; 116:9269-9274. [PMID: 31019083 PMCID: PMC6511026 DOI: 10.1073/pnas.1819316116] [Citation(s) in RCA: 93] [Impact Index Per Article: 18.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In this work we demonstrate that nonrandom mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the presence of a linear potential. In the noninteracting limit, these models show the well-known Wannier-Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient these models exhibit nonergodic behavior as indicated by their spectral and dynamical properties. These models, therefore, constitute a class of generic nonrandom models that fail to thermalize. As such, they suggest new directions for experimentally exploring and understanding the phenomena of many-body localization. We supplement our work by showing that by using machine-learning techniques the level statistics of a system may be calculated without generating and diagonalizing the Hamiltonian, which allows a generation of large statistics.
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Affiliation(s)
- Evert van Nieuwenburg
- Institute of Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125
| | - Yuval Baum
- Institute of Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125
| | - Gil Refael
- Institute of Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125
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23
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Kohlert T, Scherg S, Li X, Lüschen HP, Das Sarma S, Bloch I, Aidelsburger M. Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge. PHYSICAL REVIEW LETTERS 2019; 122:170403. [PMID: 31107070 DOI: 10.1103/physrevlett.122.170403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Indexed: 06/09/2023]
Abstract
We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-André model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase.
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Affiliation(s)
- Thomas Kohlert
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - Sebastian Scherg
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - Xiao Li
- Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, China
| | - Henrik P Lüschen
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - Sankar Das Sarma
- Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA
| | - Immanuel Bloch
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - Monika Aidelsburger
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
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24
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Lukin A, Rispoli M, Schittko R, Tai ME, Kaufman AM, Choi S, Khemani V, Léonard J, Greiner M. Probing entanglement in a many-body-localized system. SCIENCE (NEW YORK, N.Y.) 2019; 364:256-260. [PMID: 31000657 DOI: 10.1126/science.aau0818] [Citation(s) in RCA: 59] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 03/20/2019] [Indexed: 11/02/2022]
Abstract
An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system's entanglement, which is experimentally challenging to measure. We realize such a many-body-localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy, the hallmark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems.
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Affiliation(s)
- Alexander Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Matthew Rispoli
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Robert Schittko
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - M Eric Tai
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Adam M Kaufman
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Soonwon Choi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Vedika Khemani
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Julian Léonard
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.
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25
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Corcovilos TA, Mittal J. Two-dimensional optical quasicrystal potentials for ultracold atom experiments. APPLIED OPTICS 2019; 58:2256-2263. [PMID: 31044933 DOI: 10.1364/ao.58.002256] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2019] [Accepted: 02/23/2019] [Indexed: 06/09/2023]
Abstract
Quasicrystals are nonperiodic structures having no translational symmetry but nonetheless possessing long-range order. The material properties of quasicrystals, particularly their low-temperature behavior, defy easy description. We present a compact optical setup for creating quasicrystal optical potentials with five-fold symmetry using interference of nearly co-propagating beams for use in ultracold atom quantum simulation experiments. We verify the optical design through numerical simulations and demonstrate a prototype system. We also discuss generating phason excitations and quantized transport in the quasicrystal through phase modulation of the beams.
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26
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Goremykina A, Vasseur R, Serbyn M. Analytically Solvable Renormalization Group for the Many-Body Localization Transition. PHYSICAL REVIEW LETTERS 2019; 122:040601. [PMID: 30768352 DOI: 10.1103/physrevlett.122.040601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2018] [Indexed: 06/09/2023]
Abstract
We introduce a simple, exactly solvable strong-randomness renormalization group (RG) model for the many-body localization (MBL) transition in one dimension. Our approach relies on a family of RG flows parametrized by the asymmetry between thermal and localized phases. We identify the physical MBL transition in the limit of maximal asymmetry, reflecting the instability of MBL against rare thermal inclusions. We find a critical point that is localized with power-law distributed thermal inclusions. The typical size of critical inclusions remains finite at the transition, while the average size is logarithmically diverging. We propose a two-parameter scaling theory for the many-body localization transition that falls into the Kosterlitz-Thouless universality class, with the MBL phase corresponding to a stable line of fixed points with multifractal behavior.
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Affiliation(s)
- Anna Goremykina
- Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Maksym Serbyn
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
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27
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Lenarčič Z, Altman E, Rosch A. Activating Many-Body Localization in Solids by Driving with Light. PHYSICAL REVIEW LETTERS 2018; 121:267603. [PMID: 30636167 DOI: 10.1103/physrevlett.121.267603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Indexed: 06/09/2023]
Abstract
Because of the presence of phonons, many-body localization (MBL) does not occur in disordered solids, even if disorder is strong. Local conservation laws characterizing an underlying MBL phase decay due to the coupling to phonons. We show that this decay can be compensated when the system is driven out of equilibrium. The resulting variations of the local temperature provide characteristic fingerprints of an underlying MBL phase. We consider a one-dimensional disordered spin chain, which is weakly coupled to a phonon bath and weakly irradiated by white light. The irradiation has weak effects in the ergodic phase. However, if the system is in the MBL phase, irradiation induces strong temperature variations despite the coupling to phonons. Temperature variations can be used similar to an order parameter to detect MBL phases, the phase transition, and a MBL correlation length.
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Affiliation(s)
- Zala Lenarčič
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Ehud Altman
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Achim Rosch
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
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28
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Zhang SX, Yao H. Universal Properties of Many-Body Localization Transitions in Quasiperiodic Systems. PHYSICAL REVIEW LETTERS 2018; 121:206601. [PMID: 30500254 DOI: 10.1103/physrevlett.121.206601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Indexed: 06/09/2023]
Abstract
The precise nature of many-body localization (MBL) transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here, we investigate MBL transitions in one-dimensional (d=1) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent ν≈2.4, which respects the Harris-Luck bound (ν>1/d) for QP systems. Note that ν≈2.4 for QP systems also satisfies the Harris-Chayes-Chayes-Fisher-Spencer bound (ν>2/d) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure ν of QP-induced MBL transitions.
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Affiliation(s)
- Shi-Xin Zhang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
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29
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Kozarzewski M, Prelovšek P, Mierzejewski M. Spin Subdiffusion in the Disordered Hubbard Chain. PHYSICAL REVIEW LETTERS 2018; 120:246602. [PMID: 29956975 DOI: 10.1103/physrevlett.120.246602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Indexed: 06/08/2023]
Abstract
We derive and study an effective spin model that explains the anomalous spin dynamics in the one-dimensional Hubbard model with strong potential disorder. Assuming that charges are localized, we show that spins are delocalized and their subdiffusive transport originates from a singular random distribution of spin exchange interactions. The exponent relevant for the subdiffusion is determined by the Anderson localization length and the density of the electrons. Although the analytical derivations are valid for low particle density, numerical results for the full model reveal a qualitative agreement up to half filling.
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Affiliation(s)
| | - Peter Prelovšek
- J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Marcin Mierzejewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
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30
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Agarwal K, Bhatt RN, Sondhi SL. Fast Preparation of Critical Ground States Using Superluminal Fronts. PHYSICAL REVIEW LETTERS 2018; 120:210604. [PMID: 29883141 DOI: 10.1103/physrevlett.120.210604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Revised: 02/19/2018] [Indexed: 06/08/2023]
Abstract
We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally moving "front" that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. Importantly, our protocol takes time O(L) to produce the ground state of a system of size ∼L^{d} (d spatial dimensions), while a fully adiabatic protocol requires time ∼O(L^{2}) to produce a state with exponential accuracy in L. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof of concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in d=1. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin chain.
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Affiliation(s)
- Kartiek Agarwal
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08540, USA
| | - R N Bhatt
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08540, USA
| | - S L Sondhi
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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31
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Abstract
Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.
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